What is The Mean Value Theorem?(4) 中学数学教学教学方法函数正~~梁宇学中学生数学
its average velocity is 90km/ hr. Then the speedometer must have read 90km/hr at least once. Note: 1pm and 3pm represent a and b on the above formula respectively.参考: from a calculas textbook: single variable calculas-- metric version (James Stewart)
Formal Statement Suppose f(x)f(x) is continuous on [a,b][a,b], differentiable on (a,b)(a,b) and f(a)=f(b)f(a)=f(b). Then there exists some point c∈[a,b]c∈[a,b] such that f′(c)=0f′(c)=0. Understanding the Theorem Why Is Continuity Necessary? Functions that...
How important is the mean value theorem in mathematics? What does the notation lim_{x \rightarrow a^-} f(x) mean? What does the notation lim_{x \rightarrow a^+} f (x) mean? If lim_{x \rightarrow 0^-} f(x) = - \infty and lim_{x \rightarrow 0^+} what is li ...
By DeMoivre's Theorem, (2-2\sqrt{3}i)^3 = 64(\cos\pi +i\sin\pi). Let Q(x, y, z) denote the statement x^2 + y^2 = z^2. What is the truth value of Q(3, 4, 6)? a. True. b. False. What is the difference between "no truth value" and "cannot be determined" ...
Prove that if the functions g:[a,b] --> R and h:[a,b] --> R are continuous, with h(x)\geq0 for all x in [a,b] then there is a point c in (a,b) such that...
There are two versions of Cauchy's extension of the MVT. One is a little easier to interpret, but is a weaker statement. We'll start with this one, though, because once we understand the weaker version we can just make a small adjustment and we'll be able to understand the more robus...
The prime tuples conjecture does not directly say much about the value of ; however, it can be used to control differences for and not too large. Indeed, it is a famous calculation of Gallagher that for fixed , and chosen randomly from to , the quantity is distributed according to the ...
Hamilton’s quaternion number system is a non-commutative extension of the complex numbers, consisting of numbers of the form where are real numbers, and are anti-commuting square roots of with , , . While they are non-commutative, they do keep many other properties of the complex numbers: ...
What does net income mean on the income statement? How can you calculate the dollar value of gross profit? What are revenue, operating income, and net income in layman's terms? What is known as "assigned revenue? What is the equation to figure out the tax liability? What is the revenue...